verify/yosupo/number-theory/floor-sum/sum_of_floor_of_linear.test.cpp

• View this file on GitHub
• Last update: 2026-10-24 00:10:28+07:00
• Problem: https://judge.yosupo.jp/problem/sum_of_floor_of_linear

Depends on

• number-theory/floor-sum.hpp
• template.hpp

Code

#define PROBLEM "https://judge.yosupo.jp/problem/sum_of_floor_of_linear"
#include "template.hpp"
#include "number-theory/floor-sum.hpp"

int main(){
    cin.tie(nullptr)->sync_with_stdio(false);
    int t;
    cin >> t;
    while(t--){
        ll n,m,a,b;
        cin >> n >> m >> a >> b;
        cout << floor_sum(a,b,m,n-1) << "\n";
    }
}

#line 1 "verify/yosupo/number-theory/floor-sum/sum_of_floor_of_linear.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/sum_of_floor_of_linear"
#line 2 "template.hpp"
#include<bits/stdc++.h>

using namespace std;

using ll = long long;
using db = long double;
using i128 = __int128_t;
using u32 = uint32_t;
using u64 = uint64_t;
template<class T>
using PQ = priority_queue<T,vector<T>,greater<T>>;

const int INF=INT_MAX/2;
const ll LINF=LLONG_MAX/4;
const db DINF=numeric_limits<db>::infinity();
const db EPS=1e-9;
const db PI=acos(db(-1));

#define ALL(a) a.begin(),a.end()
#define RALL(a) a.rbegin(),a.rend()
#define SZ(a) (int)(a.size())
#define SORT(a) sort(ALL(a))
#define RSORT(a) sort(RALL(a))
#define REV(a) reverse(ALL(a))
#define UNI(a) a.erase(unique(ALL(a)),a.end())
#define LB(a,x) (int)(lower_bound(ALL(a),x)-a.begin())
#define UB(a,x) (int)(upper_bound(ALL(a),x)-a.begin())
#define FIND(a,x) (int)(find(ALL(a),x)-a.begin())
#define COUNT(a,x) (int)count(ALL(a),x)
#define MIN(a) *min_element(ALL(a))
#define MAX(a) *max_element(ALL(a))

template<class T,class U>
bool chmin(T &a,U b){return b<a?a=b,1:0;}
template<class T,class U>
bool chmax(T &a,U b){return a<b?a=b,1:0;}

template<class T>
T floor(T a,T b){return a/b-((a^b)<0&&a%b);}
template<class T>
T ceil(T a,T b){return a/b+((a^b)>=0&&a%b);}

int popcnt(ll x){return __builtin_popcountll(x);}
int topbit(ll x){return x==0?-1:63-__builtin_clzll(x);}
int lowbit(ll x){return x==0?-1:__builtin_ctzll(x);}

template<class T,class U>
T SUM(const U &a){return accumulate(ALL(a),T{});}
template<class T>
vector<int> argsort(const vector<T> &a){
    vector<int> p(SZ(a));
    iota(ALL(p),0);
    stable_sort(ALL(p),[&](int i,int j){return a[i]<a[j];});
    return p;
}

template<class T,size_t D=0>
struct VecBuilder{
    array<size_t,D> d;
    VecBuilder<T,D+1> operator[](size_t n)const{
        VecBuilder<T,D+1> res{};
        for(size_t i=0;i<D;i++)res.d[i]=d[i];
        res.d[D]=n;
        return res;
    }
    template<size_t I=0>
    auto build(const T &x)const{
        if constexpr(I+1==D)return vector<T>(d[I],x);
        else return vector<decltype(build<I+1>(x))>(d[I],build<I+1>(x));
    }
    auto operator()(const T &x=T())const{
        static_assert(D>0);
        return build(x);
    }
};
template<class T>
inline constexpr VecBuilder<T> VEC{};

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
mt19937_64 rng64(chrono::steady_clock::now().time_since_epoch().count());
#line 2 "number-theory/floor-sum.hpp"

/**
 * Author: Teetat T.
 * Date: 2024-09-21
 * Description: Floor sum function.
 *  $f(a, b, c, n) = \sum_{x=0}^n \lfloor \frac{ax+b}{c} \rfloor$
 *  becareful when a,b,c are negetive (use custom floor division and mod instead)
 * Time: $O(\log a)$
 */

ll floor_sum(ll a,ll b,ll c,ll n){
    ll res=n*(n+1)/2*(a/c)+(n+1)*(b/c);
    a%=c,b%=c;
    if(a==0)return res;
    ll m=(a*n+b)/c;
    return res+n*m-floor_sum(c,c-b-1,a,m-1);
}

#line 4 "verify/yosupo/number-theory/floor-sum/sum_of_floor_of_linear.test.cpp"

int main(){
    cin.tie(nullptr)->sync_with_stdio(false);
    int t;
    cin >> t;
    while(t--){
        ll n,m,a,b;
        cin >> n >> m >> a >> b;
        cout << floor_sum(a,b,m,n-1) << "\n";
    }
}

Back to top page